The diode connected transistor acts as a current sinc, and the current is determined by the series resistor. Since resistors can be made to tight tolerances, the current thru the diode connected transistor is tightly controlled. Also, the other half of the pair is a transistor that who's collector current/base-emitter voltage relationship matches the diode connected one, and since the base-emitter voltages are equal in both transistors, the output current is equal, and determined by the series resistor.